Topic: Correlation & Linear regression Subject: QTIA Software: SPSS Dr Faisal Afzal Siddiqui

1. NYC Charter
School
Performance on
the 2012-13 State
Exams
1.
Bivariate
Correlations
2.
Linear Regression
Analysis
3.
Multiple
Regression
Analysis

2. Bivariate Correlations
 Bivariate
Correlation
 Paersone
Correlation or Co-efficient of
correlation
 Scale
level of measurement

3.  p<0.05 Significant Correlation
 Researcher can be 95% confident that the
relationship between these two variables is not
due to chance

4.  Denoted
 -1
by r
≤ r ≤ +1

0 ------- ±0.3
No Relation

±0.3 ------- ±0.5
Weak Relation

±0.5 ------- ±0.8
Moderate Relation

±0.8 ------- ±1
Strong Relation

5.  1 is total positive correlation, 0 is no
correlation, and −1 is negative correlation
 The closer the value is to -1 or +1, the
stronger the association is between the
variables

6. Linear Regression Analysis

9. Outlier
 There should be no significant outliers. Outliers are simply
single data points within your data that do not follow the
usual pattern.
 The problem with outliers is that they can have a negative
effect on the regression equation that is used to predict the
value of the dependent (outcome) variable based on the
independent (predictor) variable.

10. Multiple Regression: Model Sum
a. R tells the reliability & mathematical relationship.
1. R Square (co-efficient of determination) tells the percentage of
accuracy.
2. Also percentage of variation that can not be controlled i.e.
3. (1-R Square)
i.
Adjusted R2, It can be negative & always less than or equal to R
ii. Adjusted R2 will be more useful only if the R2 is calculated based on
a sample, not the entire population
iii. Adjusted R2 increases only if the new term improves the model more
than would be expected by chance

11. ANOVA
 ANOVA
table tests whether the overall regression
model is a good fit for the data. p<0.05
 The table shows that the independent variables
statistically significantly predict the dependent
variable, F(3, 16) = 32.811, p < .0005 (i.e., the
regression model is a good fit of the data)

12. Coefficients
𝑦 = −11.823 + 0.551𝑥1 + 0.104𝑥2 + 1.989𝑥3
 How much the dependent variable varies with an
independent variable , when all other independent
variables are held constant.
 T value less than ±2 is not important
 Significant value of x
